Sincerity and Manipulation under Approval Voting
Ulle Endriss
Abstract:
Under approval voting, each voter can nominate as many candidates as
she wishes and the election winners are those candidates that are
nominated most often. A voter is said to have voted sincerely if she
prefers all those candidates she nominated to all other candidates. As
there can be a set of winning candidates rather than just a single
winner, a voter's incentives to vote sincerely will depend on what
assumptions we are willing to make regarding the principles by which
voters extend their preferences over individual candidates to
preferences over sets of candidates. We formulate two such principles,
replacement and deletion, and we show that, under approval voting, a
voter who accepts those two principles and who knows how the other
voters will vote will never have an incentive to vote insincerely. We
then discuss the consequences of this result for a number of standard
principles of preference extension in view of sincere voting under
approval voting.